June 2022 Paper 1 Q7
7 \(ABC\) is a right-angled triangle with vertices \(A\,(-1, 5)\), \(B\,(-2, 5)\) and \(C\left(-1, 5\dfrac{3}{4}\right)\)
Work out the length of \(BC\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| (\(AB =\)) 1 and (\(AC =\)) 0.75 | M1 | oe could be seen on diagram allow \(AB = -1\) and/or \(AC = -0.75\) |
| (\(BC^2 =\)) \(1^2 + \left(\dfrac{3}{4}\right)^2\) | M1dep | oe eg \((-2 - -1)^2 + \left(5\dfrac{3}{4} - 5\right)^2\) \(\sqrt{1.5625}\) or \(\sqrt{\dfrac{25}{16}}\) or \(\sqrt{1\dfrac{9}{16}}\) would imply this mark |
| (\(BC =\)) \(\dfrac{5}{4}\) or \(1\dfrac{1}{4}\) or 1.25 | A1 |
Additional guidance
| Candidates may spot it’s a \(\dfrac{3}{4}\), 1, \(\dfrac{5}{4}\) Pythagorean triple which gains the M marks and will probably go on to score all marks Ignore further rounding or truncating after correct answer seen eg \(\dfrac{5}{4}\) followed by = 1.2 would score the A mark Condone \(\dfrac{3}{4}^2\) without the brackets. Condone \(-1^2\) without the brackets | M2A1 |
| \(\dfrac{5}{4}\) followed by = 0.8 is incorrect further working | M2A0 |